where \(C_1(z)\)  is the Bessel-Clifford function of order one. A Bessel-Clifford function of order \(m\)  expands as \(C_m(x):= \sum _{k=0}^{\infty } \frac{x^k}{k!(k+m)!}\) . The explicit form (REF ) of \(\Lambda \cdot \Sigma \)  allows us to express \(C_1(\Lambda \cdot \Sigma )\)  into an \(\mathrm {SU}(2)\)  integral by the following beautiful identity [1]}
\(\int _{\mathrm {SU}(2)}\,\mathrm {d}g\, e^{\sum _{i}[z_i|g|\tilde{z}_i\rangle } =\sum _{k=0}^{\infty }{k!(k+1)!} \left( \sum _{i<j}[z_i|z_j\rangle [\tilde{z}_i|\tilde{z}_j\rangle \right)^k\,,\quad \forall z_i,\tilde{z}_i \in {\mathbb {C}}^2\,.\) 
